roy belton: the rheological and empirical characteristics of steel fibre reinforced self-compacting...

Abstract — When testing steel fibre reinforced self-compacting concrete (SFRSCC) on-site, it is not practical to determine the fundamental properties of SFRSCC by means of rheological testing. Therefore, various empirical tests have been developed to overcome this rheological shortcoming. These tests attempt to evaluate the workability of SFRSCC for its successful placement. Within this paper, the focus is on evaluating both the rheological and empirical parameters of SFRSCC with both pulverised fly ash (PFA) and ground granulated blast furnace slag (GGBS) for the partial replacement of cement (CEM II/A-L). Three self-compacting mixtures with different PFA and GGBS contents were used as reference. Each of the concretes were tested with one type of steel fibre at different contents. This was done to evaluate the influence of PFA and GGBS on both the rheological and empirical parameters of SFRSCC. In doing so, therefore, a correlation between concrete rheology and concrete workability could be determined. The results show that the use of PFA and GGBS in SFRSCC caused an overall reduction in g and an increase in h. In addition, the GGBS degraded the passing ability of SFRSCC and the workability of SFRSCC is retained for longer periods after the addition of water when using 30% PFA and 50% GGBS. Both the slump flow and slump flow t500 time showed a reasonably good correlation with, respectively, g and h, 15 minutes after the addition of mixing water, but a poor correlation existed between both the empirical and rheological parameters with an increase in time beyond 15 minutes after addition of mixing water. A good correlation was shown to exist between the L-box blocking ratio and the J-ring step of blocking for all the mixtures.

Keywords—Ground granulated blast furnace slag, Pulverised fly ash, Rheology, Self-compacting concrete, Steel fibres.

I. INTRODUCTION

ELF-COMPACTING CONCRETE (SCC) is defined as a concrete that possesses both superior flowability and a

high resistance to segregation, which must flow and fill into all the areas in the formwork, under its own weight, and without the need for conventional vibrating techniques.

S

It is well known that the use of steel fibres enhances the structural performance of concrete, mainly improved rigidity, resistance to impact and improved resistance to cracking. Intuitively, these structural enhancements can be achieved in

SCC. However, fibres are known to significantly affect the workability of concrete.

Various empirical tests have been developed to evaluate the workability of SCC (such as Slump flow, L-box and J-ring) concerning its ability to flow and fill into all the areas in the formwork, while producing an adequate uniform distribution of constituent materials. It is well known that the slump flow test is the most widely used test for evaluating the flowability of SCC. It is a modified version of the slump test, which measures two parameters: horizontal flow spread and flow time. The flow spread evaluates unconfined deformability and the flow time evaluates the rate of deformation within a confined flow distance.

According to Kasimmohammed (2014), the inverted slump cone method is the preferred choice in evaluating the workability of steel fibre reinforced concrete (SFRC) since steel fibres transmit considerable stability to a fresh concrete mass, while the inverted slump flow time is recommended rather than the traditional slump value.

Grunewald and Walraven (2001) investigated the influence of both different types of fibres and aspect ratios with various volumetric proportions on the workability of SCC. In all the mixtures, the authors report stated that the fibre type and fibre content affects the workability of SCC. Furthermore, a higher fibre aspect ratio caused a reduction in workability. The aspect ratio describes the fibre length divided its diameter. Hossain et al. (2012) discussed the influence of steel fibres on the rheological properties of SCC. They stated that increasing the fibre content increases both the plastic viscosity and yield stress.

Newman and Choo (2003) stated that the use of PFA and GGBS for the partial replacement of cement reduces the yield stress, while the use of PFA and GGBS, respectively, decreases and increases the plastic viscosity.

Tattersall and Banfill (1983) define rheology as the “science of deformation and flow of matter”. In essence rheology is concerned with relationships between stress, strain, rate of strain and time. Concrete possesses a certain resistance to flow, therefore the application of a certain force is required for concrete to flow, and that force is known as a shear stress.

Feys et al. (2008) investigated the rheological properties of SCC and compared their finding with the Bingham model. The authors reported that the stress-strain relationship of SCC is nonlinear and, therefore, shows shear thickening behavior, which can be described by the Hershel-Bulkley model. The Hershel-Bulkley model can be represented by the following equation:

τ = τ0 + kγn (1)

The Rheological Characteristics of Steel Fibre Reinforced Self-Compacting Concrete with PFA

and GGBS Roy P. Belton and Roger P. West

1

where the term τ is the shear stress, τ0 is the yield stress, k is a constant related to the consistency, γ is the imposed shear strain rate and n is the flow index which represents shear thickening (n>1) or shear thinning (n<1) and when n equals 1, the model takes the form of the Bingham model.

The torque-speed relationship in a rheometer is similar to the Hershel-Bulkley model, which can be evaluated by integrating the function speed and torsional motion by the geometry of the rheometer. This relationship is in the following form:

T = T0 + ANb (2)

where the term T is the torque, A and b are parameters that depend on the geometry of the rheometer and the concrete, N (rev/s) is the speed and T0 (N/m) is the amount of torque required to shear the concrete. By using equation (2) the nonlinear relationship of torque to speed can be determined.

0 1 2 3 4 5 6 7 80

2

4

6

8

10

12

Speed (rev/s)

To

rqu

e (N

/m)

Slope = h

T = To + ANb

g

Linear approximaton of Hershel-Bulkley model

Fig. 1. Hershel-Bulkley torque-speed relationship.

Fig. 1 illustrates the Hershel-Bulkley relationship of torque to speed. The Hershel–Bulkley parameters (A and b) are determined by plotting ln (T – T0) versus ln N. The constant A is determined by the intercept on the y-axis (ln T –T0 axis) and b is the slope of the straight-line relationship. The rheological parameter g is the intercept of this relationship on the torque axis and is related to the fundamental parameter of yield stress. The dashed black line in Fig. 1 is a linear approximation of the fitted Hershel-Bulkley model, in which the slope of this line h is related to the fundamental parameter of plastic viscosity. In this paper, the rheological properties of all the mixtures were evaluated by the rheological parameters g and h.

II.MATERIALS AND METHODS

A. Experimental program on SFRSCC with PFA and GGBS

Three self-compacting reference mixtures were developed with different compositions. Table 1 summarises these different compositions.

Table 1: Mixture composition for all reference mixtures

ComponentSeries 1 (kg/m3)

Series 2 (kg/m3)

Series 3 (kg/m3)

CEM II/A-L 580 406 290

Limestone filler 20 20 20

GGBS - - 290

PFA - 174 -

Fine aggregate 1020 1020 1020

Coarse aggregate 630 630 630

Superplasticiser (Glenium 27) 12.5 12.5 12.5

Stabiliser (RheoMatrix 100) 7.8 7.8 7.8

Water 215.5 215.5 215.5

Initially, it was assumed that the steel fibres would reduce the workability. Therefore, it was necessary to design a self-compacting reference mixture with a high degree of flowability. For this reason, both the paste and mortar content were varied by increasing the ratio of sand to aggregate and increasing the cement content, while the contents of water, superplasticiser and stabilizer were adjusted by trial and error to obtain both a high slump (700 mm) and high passing ability (J-ring: 7.25 mm). Table 1 summarises the final mix design. Next, to evaluate both the empirical and rheological parameters of SFRSCC various steel volumetric proportions of steel fibres were incorporated into each reference mix. Table 2 lists all the SFRSCC mixtures as part of this experimental program. Three SCC and 18 steel fibre reinforced mixtures were tested. Table 2: Experimental program

Steel fibre type

Steel fibre contentSCC-Series 1

(R 65/35)SCC-Series 2

(R 65/35)SCC-Series 3

(R 65/35)

0 (kg/m3) (REF) o o o5 (kg/m3) o o o10 (kg/m3) o o o15 (kg/m3) o o o20 (kg/m3) o o o25 (kg/m3) o o o30 (kg/m3) o o o

To verify the obtained empirical and rheological parameters, cubes were cast for each mixture and tested at seven-day compressive strengths. The compressive strengths for series 1 and series 2 ranged from, respectively, 64.7 – 68.1 Mpa and 33.9 – 36.8 Mpa, while series 3 ranged from 52.1 – 56.3 Mpa.B. Materials

The cement used throughout this experiment was CEM II/A-L, while also using PFA, GGBS and limestone filler (LS). The volume ratio of both the PFA GGBS was kept constant at, respectively, 70:30 and 50:50, and 95:05 for the

2

LS. Fig. 1 shows the particle size distributions of all the powders used in this experiment.

0.0001 0.001 0.01 0.1 1

0

10

20

30

40

50

60

70

80

90

100GGBS

CEM II/A-L

Fly-ash

LS

PARTICle SIZE (MM)

Per

cen

tag

e p

assi

ng

%

Fig. 2. Particle size distribution of powders

A Glenium 27 superplasticiser based on chains of a modified Polycarboxylic ether complex was used to achieve an adequate workability. RheoMatrix 100, an aqueous solution of a high-molecular weight synthetic copolymer was used to modify the viscosity and cohesion of the mixtures. Ordinary tap water was used as mixing water in all the mixtures. One steel fibre (SF) type with hooked ends (R 65/35) were used in all the SFRSCC mixtures. The 65 is the aspect ratio and the 35 in the fibre length in mm. Both locally available sand and gravel were used. Crushed stone aggregates of nominal maximum size 10 mm were used as coarse aggregates. Fig. 3 shows the particle size distributions of all the aggregates.

0.01 0.1 1 10 100

0

10

20

30

40

50

60

70

80

90

100Sand B & Coarse aggregates

Sand B

Particle size mm

Per

cen

tag

e p

assi

ng

%

Series 1Series 2Series 3

Fig. 3. Particle size distribution of the aggregates

C. Mix procedure

A free-fall mixer was used throughout this study. The following mix procedure was adopted:

Coarse aggregates and 40% water for 10 s. Fine aggregates and powders for 60 s. Superplasticiser and 50% water for 20 s. Stabiliser and 10% water for 20 s. Resting period of 600 s. Mixing period of 60 s. Steel fibres for 60 s.

D. Test methods

The quantitative empirical tests used in this experiment were the slump flow, L-box and J-ring. The inverted slump flow cone method was used in this experimental program. After lifting the slump flow cone, the slump flow is the mean horizontal flow spread and the t500 time is the time taken to reach a flow spread of 500 mm. Both the L-box and J-ring

Fig. 4. Empirical test methods: (i) L-box (ii) Slump flow and (iii) inverted J-ring.

were used to assess the passing ability. The concrete in the L-box is placed in the vertical channel. Opening the gate allows the concrete to flow through the vertical bar spacings and into the horizontal channel, the height of concrete in both the vertical and horizontal channel are then expressed as a ratio, known as the passing ratio, where an acceptable passing ratio ranges from 0.8 – 1.0. In the J-ring, the inverted cone is lifted, the t500 time recorded, that is, the time for the concrete to reach a 500 mm spread distance and its passing ability is assessed by the average height of concrete at four points around the ring minus the height at the central position and expressed in mm, where an acceptable passing value ranges from 0 – 10 mm.

The rheological tests were performed with the Tattersall Two-point workability apparatus (TWT), in particular, the MK II model, which involves an axial impeller with four angled blades positioned in a helical arrangement around a central drive shaft. The schematic diagram is shown in Fig. 5. According to Tattersall and Banfill (1983) this helical arrangement raises the concrete while also allowing the concrete to fall back through the gaps, i.e., minimises the effects of both segregation and bleeding. A cylindrical bowl containing the concrete is supported by means of an adjustable arm. This allows the concrete sample to be raised and supported both during testing and following the testing regime. The effective height between the top of the bowl and the shearing surface is 75 mm. Before initiating the testing regime, the apparatus must run for 30 minutes to allow the oils (both hydraulic and gear) to reach their operating temperatures, and

3

Fig. 5. Schematic diagram of TWT.

during the warmup period, the recommended speed is 0.7 rev/s. However, Tattersall (2003) recommended speeds of 3.0 rev/s because at a warmup speed of 0.7 rev/s the idling pressure can change even after 80 minutes. In essence, the torque-speed relationship for the concrete undergoing testing is determined by reducing the speed (rev/s) from 0.7 to 0.3 rev/s at various speed intervals, while recording the resulting pressure (lb/in2) at these intervals of speed. In doing so, the torque intercept and slope and, therefore, the rheological parameters g and h are determined.

The following testing regime was performed in order to determine the influence of time on both the empirical and rheological parameters, that is, an increase in time after the addition of both mixing water and cementitious materials.

Table 3: Testing regime for time evolution of empirical and rheological parameters.

Sequence

Regime-1 (15 min after

addition of water)

Regime-2 (30 - 65 min after addition of

water)

Regime-3 (65 - 95 min after addition of

water)

1 TWT TWT TWT

2 Slump flow Slump flow Slump flow

3 L-box L-box L-box

4 J-ring J-ring J-ring

First, the rheological parameters g and h were determined with the TWT apparatus, then followed by the empirical tests, i.e., Slump flow, L-box and J-ring. This was carried three times at different times after the addition of mixing water. Table 3 lists the three testing regimes and sequence of tests.

Immediately after each test (i.e. TWT, Slump flow, L-box, J-ring) for all the mixtures, the concrete was remixed in the mixer with the remaining concrete for approximately 15 – 20 s, in order to try and eliminate the effects of segregation cause by the MK II apparatus and to promote an even distribution of fibres throughout all the mixture undergoing testing.

III. RESULTS AND DISCUSSION

A. Effect of SF, PFA and GGBS on rheology

Rheological testing was performed on all the mixtures, 15 min after the addition of mixing water. In considering all the possible functional relationships for all the mixtures, the polynomial function seems to produce the best fit correlation between torque and speed. The slopes of these relationships and, therefore, the h parameters were determined by a linear approximation of the fitted Hershel-Bulkley model.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

0

1

2

3

4

5

6

7

8

9

10 SCC-1, 15 minSCC-2, 15 minSCC-3, 15 minSCC-4, 15 minSCC-5, 15 minSCC-6, 15 minSCC-7, 15 min

Speed (rev/s)T

orq

ue

(N/m

)

Series 1 (CEM II/A-L)

0 kg/m3 SF5 kg/m3 SF

10 kg/m3 SF15 kg/m3 SF20 kg/m3 SF25 kg/m3 SF30 kg/m3 SF

Fig. 9. Fitted Hershel-Bulkley models for SCC-1 to SCC-7, 15 min after the addition of water.

As the torque-speed relationships for all the mixtures showed nonlinear behavior, the Hershel-Bulkley model was used to represent these relationships. Fig. 9 – Fig. 11 illustrates these fitted Hershel-Bulkley relationships for all the mixtures corresponding to a TWT carried out 15 min after the addition of water. In Fig. 9 – Fig. 11, SCC-1 to SCC-7 represents series-1 with 0kg/m3 – 30kg/m3 of SF, SCC-8 to SCC-14 represents series-2 with 0kg/m3 – 30kg/m3 of SF and SCC-15 to SCC-21 represents series-3 with 0kg/m3 – 30kg/m3, respectively.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

0

1

2

3

4

5

6

7


Speed (rev/s)

To

rqu

e (N

/m)

Series 2 (PFA)




TWT bowl

Vane arrangement

Speed gauge

Pressure gauge

Rack and pinion

4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.30

2

4

6

8

10


Speed (rev/s)

Torq

ue (N

/m)

Series 3 (GGBS)




From Fig. 9 – Fig. 11, it may be observed that the rheological parameters g and h are increasing with an increase in steel fibre content. The variation of g and h with steel fibre content is presented in Fig. 12 and Fig. 13. The x-axis in both Fig. 12 and Fig. 13 represents the steel fibre content, i.e., 0kg/m3 – 30kg/m3.

0 5 10 15 20 25 30

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

SFRSCC

SFRSCC with PFA

SFRSCC with GGBS

Steel fibre content (kg/m3)

Rh

eolo

gic

al p

aram

eter

, g

Fig. 12. Effect of PFA and GGBS on the rheological parameter g, 15 min after the addition of mixing water.

0 5 10 15 20 25 30

0

1

2

3

4

5

6

7

SFRSCC

SFRSCC with PFA

SFRSCC with GGBS

Steel fibre content (kg/m3)

Rh

eolo

gic

al

pa

ram

eter

, h

Fig. 13. Effect of PFA and GGBS on the rheological parameter h, 15 min after the addition of mixing water.

It may be observed that, in both cases, the rheological parameters g and h increase with an increase in steel fibre content. In addition, the parameter g decreases when using PFA and GGBS CEM II/A-L cement replacements in

SFRSCC. However, the parameter g is somewhat constant for both the SFRSCC and the SFRSCC with 50% GGBS CEM II/A-L replacement at SF contents ranging from 0 – 15kg/m3. In Fig. 13, it may be observed that the parameter h increases when using 30% PFA and 50% GGBS CEM II/A-L replacements in SFRSCC.

Fig. 14 – Fig. 16 illustrates the variation of g and h with increasing steel fibre contents for SCC-1 to SCC-21. In addition, the obtained correlation coefficients for SCC-1 to SCC-21, 15 min after the addition of water are illustrated. As shown in Fig. 14, a second order polynomial function seems to yield the best-fit correlation between the rheological parameters g and h, with a best-fit correlation, R2, of 0.855. It is the author’s opinion that the obtained rheological parameters (g and h) associated with SCC-7 are most likely underestimated, because during testing a significant degree of segregation was encountered. Nevertheless, the results for SCC-7 were included in this analysis.

0 0.4 0.8 1.2 1.6 2

0

1

2

3

4

5

6

0 kg/m3 SF

5 kg/m3 SF

10 kg/m3 SF

15 kg/m3 SF

25 kg/m3 SF

30 kg/m3 SF

f(x) = 1.938918586077 x² − 2.764379799306 x + 3.601391264332R² = 0.855214984129356

Rheological parameter, g

Rhe

olog

ical

par

amet

er, h Series 1 (CEM II/A-

L)

Fig. 14. Variation of g and h with increasing steel fibre (SF) contents for SCC-1 to SCC-7, 15 min after the addition of water.

0.4 0.6 0.8 1 1.2 1.4

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

30 kg/m3 SF

0 kg/m3 SF

5 kg/m3 SF

10 kg/m3 SF

15 kg/m3 SF

20 kg/m3 SF

25 kg/m3 SF

f(x) = 2.92317420582468 exp( 0.386343269536802 x )R² = 0.84127249784967


Rhe

olog

ical

par

amet

er, h

Series 2 (PFA)


From Fig. 14 – Fig. 15, it may be observed that an exponential function seems to yield the best fit correlation between g and h for SCC-8 to SCC-13, and SCC-15 to SCC-20 with best fit correlations of, respectively, 0.841 and 0.708. Also, the torque-speed relationships and, hence, the obtained parameters g and h for SCC-14 and SCC-21 were not included in this

5

analysis, as the obtained torque-speed relationship for these data points possessed a significant degree of nonlinearity, which is an indication of segregation. Furthermore, during rheological testing a high degree of segregation was encountered (i.e., there was a significant amount of coarse aggregates and steel fibres stuck to the bottom of the mixing bowl) in SCC-14 and SCC-21, 15 min after the addition of water.

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4

4

4.5

5

5.5

6

6.5

7


5 kg/m3 SF

10 kg/m3 SF


25 kg/m3 SF

f(x) = 4.36176524110028 exp( 0.272251805122281 x )R² = 0.707981915120566


Rhe

olog

ical

par

amet

er, h

Series 3 (GGBS)


B. Empirical and rheological parameters for SFRSCC

The relationship between the J-ring step of blocking and L-box blocking ratio for all the mixtures (i.e. 15 to 95 min after the addition of water) is presented in Fig. 17. From Fig. 17, it may be observed that a linear relationship exists between these empirical values with a correlation coefficient (R2) of 0.83 and a coefficient of variation of -2.13, which suggests that the J-ring step of blocking is inversely related to the L-box blocking ratio. Therefore, as the J-ring step of blocking (mm) decreases, L-box ratio increases. The following empirical relation may be obtained by least square regression:

LB = 1.09-0.029(JR) (3)

where JR is the J-ring step of blocking in mm and LB is the L-box blocking ratio.

0 10 20 30 40 50 60 70

0

0.2

0.4

0.6

0.8

1

1.2

f(x) = − 0.0290657251388758 x + 1.09101341644886R² = 0.829717455591301

SCC-1 to SCC-21, 15 minSCC-1 to SCC-21, 30 - 65 minSCC-1 to SCC-21, 60 - 95 min

J-ring, step of blocking (mm)

L-b

ox

blo

ckin

g r

atio

(H

2/H

1)

CV = -2.13

Fig. 17. Variation of J-ring step of blocking with L-box blocking ratio for SCC-1 to SCC-21, 15 to 95 min after the addition of water.

The variation of slump flow and slump flow t500 time with, respectively, g and h is presented in Fig. 18 and Fig. 19. From Fig. 18, it may be observed that a poor relationship exists between slump flow and g, 15 to 95 min after the addition of water with a correlation coefficient (R2) of 0.22 and a coefficient of variation (CV) of -9.98. From Fig. 19, it shows a correlation coefficient of 0.3 and a coefficient of variation of -1.0 between slump flow t500 time and h for all the mixtures tested at 15 to 95 min after the addition of water.

0 0.5 1 1.5 2 2.5 3 3.5

500

550

600

650

700

750

800

f(x) = − 35.4682188203232 x + 734.669158742188R² = 0.21517400976868

SCC-1 to SCC-20, 15 min


Slu

mp

flo

w s

pre

ad (

mm

)

CV = -9.98

Fig. 18. Variation of Slump flow with g for SCC-1 to SCC-21, 15 to 95 min after the addition of water.

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

0

2

4

6

8

10

12

f(x) = 0.614155144502876 x + 0.836509601156264R² = 0.30281072967086

SCC-1 to SCC-20, 15 min

SCC-1 to SCC-20, 30 - 65 min

Rheological parameter, h

Slu

mp

flo

w,

t50

0 t

ime

(sec

)

CV = 1.0

Fig. 19. Variation of Slump flow t500 time with h for SCC-1 to SCC-21, 15 to 95 min after the addition of water.

The variation of J-ring step of blocking with blocking ratio, 15 min after the addition of water is presented in Fig. 20. It may be observed that there exists a linear relationship between these empirical parameters with a correlation coefficient (R2) of 0.9. In addition, the obtained coefficient of variation (CV) is -1.043, which suggests that the J-ring step of blocking is inversely related to the L-box blocking ratio. Therefore, as the J-ring step of blocking (mm) decreases, L-box ratio increases. The following empirical relation may be obtained by least square regression:

LB = 1.098-0.027(JR) (4)

6

where JR is the J-ring step of blocking in mm and LB is the L-box blocking ratio.

0 5 10 15 20 25 30 35

0

0.2

0.4

0.6

0.8

1

1.2

f(x) = − 0.0272018128551079 x + 1.0984591157247R² = 0.899463415391305

J-ring, step of blocking (mm)

L-b

ox

blo

ckin

g r

atio

(H

2/H

1)

CV = -1.043

Fig. 20. Variation of L-box with J-ring for SCC-1 to SCC-21, 15 min after the addition of water.

The variation of slump flow and slump t500 time with, respectively, g and h is presented in Fig. 21 and Fig. 22. It may also be observed from Fig. 21 that there exists a linear relationship between slump flow and g with an obtained correlation coefficient (R2) of 0.8 and a coefficient of variation (CV) of -4.57, which suggests that g is inversely related to slump flow.

0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

600

620

640

660

680

700

720

740

SCC-14

SCC-21

f(x) = − 43.0242709698268 x + 730.885232433187R² = 0.796421966228956


Slu

mp

-flo

w s

pre

ad v

alu

e (m

m)

CV = -4.57

Fig. 21. Variation of Slump flow with rheological parameter g for SCC-1 to SCC-21, 15 min after the addition of water.

As the rheological parameter g decreases, slump flow increases. In addition, the obtained parameters g and h for SCC-7 and SCC-21 were not included in this analysis, as a significant amount of coarse aggregates and steel fibres had settled to the bottom of the TWT bowl. The following empirical relation may be obtained by least square regression:

SF = 730.9-43(g) (5)

where SF is the slump flow in mm and g is the rheological parameter in N/mm, which is related to yield stress.

It may be observed from Fig. 22 that there also exists a

relationship between slump flow t500 time and h with a correlation coefficient of 0.835 and a coefficient of variation of 0.72, which suggests that the slump flow t500 time is positively related to the rheological parameter h. Therefore, the following empirical relationship may be obtained by least square regression:

h = 1.63(t500)-0.68 (6)

where h is the slope of the torque-speed relationship (i.e., the slope of the linear approximation of the Hershel-Bulkley model, which is related to plastic viscosity and t500 is the slump flow t500 time in seconds.

1.5 2 2.5 3 3.5 4 4.5

0

1

2

3

4

5

6

7

SCC-14

SCC-21f(x) = 1.62751162621118 x − 0.679462981188106R² = 0.834719873080687

Slump-flow, t500 time (sec)

Rh

eolo

gic

al p

aram

eter

, h

CV = 0.72

Fig. 22. Variation of Slump flow t500 time with h for SCC-1 to SCC-21, 15 min after the addition of water.

IV. CONCLUSIONS

Based on the results presented in this paper, the following conclusion can be drawn:

There is a good correlation between the J-ring step of blocking and L-box blocking ratio for all the mixtures at testing times corresponding to 15 to 95 min after the addition of both mixing water and cementitious materials. J-ring step of blocking decreases linearly as L-box blocking increases.

A good correlation between inverted slump flow and g for all the mixtures, 15 min after the addition of both mixing water and cementitious materials. Also, the parameter g decreases as inverted slump flow increases.

A good correlation between inverted slump flow t500

time and h, 15 min after the addition of water and cementitious materials. In addition, the parameter h increases as inverted slump flow t500 time increases.

There is a poor correlation between g and inverted slump flow, h and inverted slump flow t500 time, 15 to 95 min after the addition of water and cementitious materials.

The rheological parameters g and h increased with an increase in steel fibres content. In addition, there is a good correlation between the relative

7

parameters g and h with increasing steel fibre contents.

Using 30% PFA and 50% GGBS CEM II/A-L cement replacements reduced the parameter g, while causing an increase in h.

The workability of SFRSCC is retained for longer periods when using 30% PFA and 50% GGBS CEM II/A-L cement replacements.

V. REFERENCES

[1] Kasimmohammed, A. (2014). Flexural and shear performance of high dosage steel fibre reinforced concrete in suspended slabs.

[2] Grünewald, S., and Walraven, J. C. (2001). Parameter-study on the influence of steel fibres and coarse aggregate content on the fresh properties of self-compacting concrete. Cement and Concrete Research, 31(12), 1793-1798.

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